If you are a PC member, you can use NWA and DL clubs worldwide regardless of what type of ticket you are using to travel. My experience is that none of the three have any particular advantage regarding quality of snacks. If they give away free drinks in the USA, all of the clubs have to reconcile with local alcohol laws, as well as the airports' desire to protect their commercial restaurants and bars that pay hefty concession fees. That is one reason for the prominent "no outside food" signs in all of the clubs.

PC members can use domestic Alasaka clubs if traveling on an Alaska ticket, regardless of class.

All three airlines use other clubs at some international airports. My experience has been that you need to be traveling on a ticket from an airline that uses the airport to use the club. For example, NWA uses the Thai Airways club in Singapore, and CO PC members are welcome when traveling on NWA, but not another airline. I was going to Manila on Jetstar Asia from Singapore and my PC card was politely declined.

I think the general rule of thumb should be to belong to the club of he airline that you use the most because their hub airport clubs are usually very nice facilities.

Hope this helps.